We present a high order, robust, and stable shock-capturing technique for finite element approximations of ideal MHD. The method uses continuous Lagrange polynomials in space and explicit Runge-Kutta schemes in time. The shock-capturing term is based on the residual of MHD which tracks the shock and discontinuity positions, and adds a sufficient amount of viscosity to stabilize them. The method is tested up to third order polynomial spaces and an expected fourth-order convergence rate is obtained for smooth problems. Several discontinuous benchmarks such as Orszag-Tang, MHD rotor, Brio-Wu problems are solved in one, two, and three spatial dimensions. Sharp shocks and discontinuity resolutions are obtained.

翻译：对于理想MHD的有限元素近似值,我们提出了一个高顺序、稳健和稳定的冲击摄取技术。该方法在空间使用连续的Lagrange多级模拟器,在时间上使用明确的龙格-库塔方案。冲击摄取术语以MHD的剩余值为基础,该剩余值跟踪冲击和不连续位置,并增加足够的粘度以稳定这些位置。该方法经过测试,达到第三顺序多级空间,并有望为平滑的问题获得第四阶趋同率。一些不连续的基准,如Orszag-Tang、MHD转盘、Brio-Wu问题,在一、二和三个空间层面得到解决。获得了剧烈冲击和不连续解决方案。